Luogu4402 机械排序

题目蓝链

Description

给你一个长度为\(n\)的序列，你要对它进行操作，规则如下

第\(i\)次操作时，找到区间\([1, n]\)中第\(i\)小的数的位置\(p_i\)，并翻转区间\([i, p_i]\)

最后输出操作序列\(p_i\)

Solution

很久没有做过\(Splay\)的题目了，来打个板子复习一下

我们可以把题意转换一下：第\(i\)次操作时，找到区间\([i, n]\)中最小的数的位置\(p_i\)，并翻转区间\([i, p_i]\)

然后这相当于就是一个排序 虽然我没用这个做法

我的做法特别简单粗暴，就是照着题意模拟

每次直接找整段区间最小值的位置，然后用\(Splay\)模拟题目的翻转，然后把这个最小值设为\(inf\)

\(p_i​\)序列就边操作边输出就可以了

Code

#include <bits/stdc++.h>

using namespace std;

#define fst first
#define snd second
#define mp make_pair
#define squ(x) ((LL)(x) * (x))
#define debug(...) fprintf(stderr, __VA_ARGS__)

typedef long long LL;
typedef pair<int, int> pii;

template<typename T> inline bool chkmax(T &a, const T &b) { return a < b ? a = b, 1 : 0; }
template<typename T> inline bool chkmin(T &a, const T &b) { return a > b ? a = b, 1 : 0; }

inline int read() {
    int sum = 0, fg = 1; char c = getchar();
    for (; !isdigit(c); c = getchar()) if (c == '-') fg = -1;
    for (; isdigit(c); c = getchar()) sum = (sum << 3) + (sum << 1) + (c ^ 0x30);
    return fg * sum;
}

const int maxn = 1e5 + 10;
const int inf = 1e9;

int n, a[maxn];

namespace Splay {
    int rt;
    struct node {
        int f, son[2], v, s, sz;
        bool rev;
        node(): v(inf), s(inf) { }
    }A[maxn];
#define ls(x) A[x].son[0]
#define rs(x) A[x].son[1]
#define fa(x) A[x].f
    inline void push_up(int x) { A[x].s = min(min(A[ls(x)].s, A[rs(x)].s), A[x].v), A[x].sz = A[ls(x)].sz + A[rs(x)].sz + 1; }
    inline void push_down(int x) {
        if (A[x].rev) {
            swap(ls(x), rs(x));
            A[ls(x)].rev ^= 1, A[rs(x)].rev ^= 1, A[x].rev = 0;
        }
    }
    inline bool chk(int x) { return rs(fa(x)) == x; }
    inline void link(int x, int y, int f) { fa(x) = y, A[y].son[f] = x; }
    inline void rotate(int x) {
        int f = fa(x), dx = chk(x), df = chk(f);
        link(A[x].son[dx ^ 1], f, dx);
        link(x, fa(f), df);
        link(f, x, dx ^ 1);
        push_up(f), push_up(x);
    }
    inline void splay(int x, int y) {
        static int S[maxn]; S[S[0] = 1] = x;
        for (int _x = x; _x; _x = fa(_x)) S[++S[0]] = _x;
        while (S[0]) push_down(S[S[0]--]);
        while (fa(x) != y) { if (fa(fa(x)) != y) rotate(chk(x) == chk(fa(x)) ? fa(x) : x); rotate(x); }
        if (!y) rt = x; /**/
    }
    inline void build(int &x, int l, int r) {
        if (l > r) return;
        int mid = (l + r) >> 1;
        A[x = mid].v = a[mid - 1];
        build(ls(x), l, mid - 1), build(rs(x), mid + 1, r);
        if (ls(x)) fa(ls(x)) = x;
        if (rs(x)) fa(rs(x)) = x;
        push_up(x);
    }
    inline int Rank(int k) {
        int x = rt;
        while (1) {
            push_down(x);
            int tot = A[ls(x)].sz + 1;
            if (k == tot) break; /**/
            if (k < tot) x = ls(x);
            else x = rs(x), k -= tot;
        }
        return x;
    }
    inline void reverse(int x, int y) {
        --x, ++y;
        x = Rank(x), y = Rank(y);
        splay(x, 0), splay(y, x);
        A[ls(y)].rev ^= 1;
    }
    inline void change(int x) {
        x = Rank(x);
        A[x].v = inf;
        while (x) push_up(x), x = fa(x);
    }
    inline int query() {
        int x = rt, res = 0;
        while (ls(x) || rs(x)) {
            push_down(x);
            if (A[x].v == A[x].s) { res += A[ls(x)].sz; break; } /**/
            x = (A[ls(x)].s < A[rs(x)].s ? ls(x) : (res += A[ls(x)].sz + 1, rs(x)));
        }
        return res + 1;
    }
}

int main() {
#ifdef xunzhen
    freopen("sort.in", "r", stdin);
    freopen("sort.out", "w", stdout);
#endif

    static pii p[maxn];
    n = read();
    for (int i = 1; i <= n; i++) p[i] = mp(a[i] = read(), i);
    sort(p + 1, p + n + 1);
    for (int i = 1; i <= n; i++) a[p[i].snd] = i;
    a[0] = a[n + 1] = inf;

    Splay::build(Splay::rt, 1, n + 2);

    for (int i = 2; i <= n + 1; i++) {
        int x = Splay::query();
        Splay::reverse(i, x);
        Splay::change(i);
        printf("%d%c", x - 1, i <= n ? ' ' : '\n');
    }

    return 0;
}